The woman, identified as 27-year-old Elisabeth Matthes, was recovered on a rocky scree at 2,200 metres (7,200 feet) of altitude, to the north of the mountain resort of Campo Imperatore.
Her rucksack was found 200 metres higher up the mountain.
The AGI news agency said the woman had checked into the Campo Imperatore hotel on Monday but had not been there since going out shortly after her arrival.
Staff raised the alarm when she did not come back for dinner, having leftsome of her belongings in her room.
The hotel is famous as the place where Italian dictator Benito Mussolini was briefly imprisoned in August 1943 before he was liberated in a daring raid by German commandoes.
The area around Gran Sasso, which rises to a peak at 2,912 metres, is popular with hikers in the summer but is considered dangerous walking territory from early October onwards.
AGI reported that the local police had ruled out the involvement of any other party in the woman's death. The corpse was to be evacuated by helicopter with formal identification set to take place on Monday.